Information on Result #2227776
Linear OA(337, 19693, F3, 6) (dual of [19693, 19656, 7]-code), using 1 times truncation based on linear OA(338, 19694, F3, 7) (dual of [19694, 19656, 8]-code), using
- construction X4 applied to Ce(6) ⊂ Ce(4) [i] based on
- linear OA(337, 19683, F3, 7) (dual of [19683, 19646, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(328, 19683, F3, 5) (dual of [19683, 19655, 6]-code), using an extension Ce(4) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,4], and designed minimum distance d ≥ |I|+1 = 5 [i]
- linear OA(310, 11, F3, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,3)), using
- dual of repetition code with length 11 [i]
- linear OA(31, 11, F3, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
The following results depend on this result:
| Result | This result only | Method | ||
|---|---|---|---|---|
| 1 | Linear OOA(337, 19693, F3, 2, 6) (dual of [(19693, 2), 39349, 7]-NRT-code) | [i] | Embedding of OOA with Gilbert–Varšamov Bound | |
| 2 | Linear OOA(337, 19693, F3, 3, 6) (dual of [(19693, 3), 59042, 7]-NRT-code) | [i] | ||
| 3 | Linear OOA(337, 19693, F3, 4, 6) (dual of [(19693, 4), 78735, 7]-NRT-code) | [i] | ||
| 4 | Linear OOA(337, 19693, F3, 5, 6) (dual of [(19693, 5), 98428, 7]-NRT-code) | [i] | ||
| 5 | Linear OOA(337, 9846, F3, 2, 6) (dual of [(9846, 2), 19655, 7]-NRT-code) | [i] | OOA Folding | |
| 6 | Linear OOA(337, 6564, F3, 3, 6) (dual of [(6564, 3), 19655, 7]-NRT-code) | [i] | ||
| 7 | Linear OOA(337, 6564, F3, 4, 6) (dual of [(6564, 4), 26219, 7]-NRT-code) | [i] | OA Folding and Stacking | |
| 8 | Linear OOA(337, 6564, F3, 5, 6) (dual of [(6564, 5), 32783, 7]-NRT-code) | [i] | ||